Puzzle: The Monty Hall problem

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If you've already heard this one please let those who haven't bat it around first.

And no fair Googling the answer and then posting like you are some damn smarty pants.

Once upon a time there was a game show called "Let's Make a Deal". It was hosted by the prototypical game show host Monty Hall. For the better part of the show he would be out in the audience playing various games where they would have to choose between hidden prizes, or they would have to choose whether to give up a known prize for a mystery prize...that kind of thing. Sometimes to taunt the players he would reveal an unselected prize.

Anyway...here is the puzzle based on that show...

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door No. 1, and Monty, who always knows what's behind the doors, opens door No. 3, which has a goat. Monty then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?



- Phil

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